Modularity on vertex operator algebras arising from semisimple primary vectors
نویسنده
چکیده
In this article, using an idea of the physics superselection principal, we study a modularity on vertex operator algebras arising from semisimple primary vectors. We generalizes the theta functions on vertex operator algebras and prove that the internal automorphisms do not change the genus one twisted conformal blocks.
منابع مشابه
Simple currents and extensions of vertex operator algebras
We consider how a vertex operator algebra can be extended to an abelian intertwining algebra by a family of weak twisted modules which are simple currents associated with semisimple weight one primary vectors. In the case that the extension is again a vertex operator algebra, the rationality of the extended algebra is discussed. These results are applied to affine Kac-Moody algebras in order to...
متن کاملExceptional Vertex Operator Algebras and the Virasoro Algebra
We consider exceptional vertex operator algebras for which particular Casimir vectors constructed from the primary vectors of lowest conformal weight are Virasoro descendants of the vacuum. We discuss constraints on these theories that follow from an analysis of appropriate genus zero and genus one two point correlation functions. We find explicit differential equations for the partition functi...
متن کاملRepresentations of vertex operator algebras
This paper is an exposition of the representation theory of vertex operator algebras in terms of associative algebras An(V ) and their bimodules. A new result on the rationality is given. That is, a simple vertex operator algebra V is rational if and only if its Zhu algebra A(V ) is a semisimple associative algebra. 2000MSC:17B69
متن کاملOn abelian coset generalized vertex algebras
This paper studies the algebraic aspect of a general abelian coset theory with [DL2] as our main motivation. It is proved that the vacuum space ΩV (or the space of highest weight vectors) of a Heisenberg algebra in a general vertex operator algebra V has a natural generalized vertex algebra structure in the sense of [DL2] and that the vacuum space ΩW of a V -module W is a natural ΩV -module. Th...
متن کاملVertex Operator Algebras And
Let V be a vertex operator algebra. We construct a sequence of associative algebras A n (V) (n = 0; 1; 2; :::) such that A n (V) is a quotient of A n+1 (V) and a pair of functors between the category of A n (V)-modules which are not A n?1 (V)-modules and the category of admissible V-modules. These functors exhibit a bijection between the simple modules in each category. We also show that V is r...
متن کامل